# Coefficients of friction proportional?

1. Nov 28, 2015

### zpatenaude37

If you were to calculate work done by rolling friction of a wood sphere rolling down an incline and compare it to work done by friction of a wood block sliding down an incline, are the values for the coefficient of rolling and kinetic friction somehow proportional to each other?

This is for a project and I want to be able to show whether or not the additional surface area of a block affects the work done by friction. I have calculated values for the coefficients of kinetic and rolling friction from the data I have that I got using video software but I don't think I can correlate the two.

2. Nov 28, 2015

### richard.li

Hi, according to the Mechanical Engineering Handbook i read a few weeks ago, rolling friction depends on the radius of sphere and materials in contact, i.e. larger sphere usually has smaller friction coefficient.
While kinetic friction is purely dependent on the materials in contact. For you idea of having additional surface area for a block simply will not affect the kinetic friction.

So i would say rolling friction and kinetic friction coefficient does not have a specific correlation.

3. Nov 30, 2015

### jbriggs444

When you speak of "rolling friction", are you referring, for instance, to the force between a car tires and the road when the brakes are applied at the maximum short of causing a skid? Or are you referring to the retarding force from the tires as a car coasts to a stop with well-oiled bearings and no brakes? The former is that I would call "static friction". The latter is that I would call "rolling resistance".

4. Nov 30, 2015

### zpatenaude37

Yes rolling resistance.
For example:
at the start of rolling down an incline the total energy in the system is
mgy
for a block the final is:
1/2mv^2
for a sphere is:
1/2mv^2 + 1/2Iw^2

initial energy - final energy = thermal energy = work done by friction = mu*n*d

For the sphere my data showed mu = .11
For a cylinder of the same material mu = .11
For the block sliding mu = 0.46

Is there any way to compare the block to the cylinder and sphere to say its proportional?

5. Nov 30, 2015

### nasu

With just two values you cannot show anything about proportionality.